The bank decision in Brussels was aimed at helping Spain, which sought a rescue to help its troubled banks.
European Council President Herman Van Rompuy called it a "breakthrough that banks can be recapitalized directly."
In addition, the leaders agreed that EU countries that were following budget rules could apply for bailouts that would not come with the stringent conditions that have accompanied previous EU bailouts a recognition, said Italian Premier Mario Monti, who pushed for the deal, of the work such countries were already doing in reforming their budgets.
Monti said Italy did not intend to apply for a bailout.
Still, Van Rompuy said the bailout agreement was important.
"We are opening the possibilities for countries that are well-behaving to make use of financial stability instruments, the EFSF and ESM, in order to reassure markets and get again some stability around some of the sovereign bonds of our member states," he said, referring to two bailout funds set up by the EU.
That meant, he said, that there would not be any more countries struggling under the stern conditions that have been imposed on previous EU countries that received bailouts an apparently sharp change in EU policy.
EU leaders agreed Thursday night to devote 120 billion euros in stimulus to encourage growth and create jobs. France had pushed for the growth package, arguing that austerity measures imposed to stem Europe's debt crisis were stifling growth and making it worse.
German Chancellor Angela Merkel said after the meetings broke up soon before dawn that she was "very satisfied that we took good decisions on growth."
Van Rompuy said leaders of the 17-nation eurozone also agreed to a joint banking supervisory body. And he said the leaders of the full 27-member European Union agreed to a general long-term plan for a tighter budgetary and political union.
The importance of recapitalizing banks directly became evident when Spain asked for money for its shaky banks. Under current rules the bailout loan had to be made to the government, which would then lend it on to the banks. But having that debt on the government's books spooked investors, who began demanding higher interest rates for lending money to the government.
The result was rates that would have been unsustainable in the long term. Lending the money directly to the banks would avoid putting that debt on the government's books.
The leaders agreed on "the four building blocks" of a tighter European Union but said they wouldn't start pinning down details until a report in October. The building blocks were laid out in a sweeping document presented by Van Rompuy and colleagues earlier this week that included sharing debt in the form of jointly issued eurobonds.
Van Rompuy said the report expected in October would be "a specific and time-bound roadmap for the achievement of a genuine economic and monetary union."
"The aim is to make the euro an irreversible project," he said.
He did not say Friday, however, whether the general agreement on the tighter union included a firm commitment on eurobonds from Germany which has firmly opposed sharing debt with more profligate countries such as Greece.
Analysts said the proposals at the summit in Brussels represented credible steps forward in the region's efforts to contain a debt and financial crisis and to help struggling countries like Greece and Spain, whose economies are hobbled by recession and severe borrowing problems.
"Although the EU summit is still stuck on major issues including joint debt, euro bonds ... the EU has laid out a long term plan in principle that can solve the problem if they can get all the leaders agreed on the details," said Jackson Wong, vice president at Tanrich Securities in Hong Kong.
"We don't expect a magical formula that can solve the problem right out from the EU summit. However, if we can see the stances from all the leaders, especially from Germany that they are heading to the right direction I think going forward, it should be OK."
The summit wraps up later Friday.